autoregressie

*The author of this computation has been verified*

R Software Module: /rwasp_multipleregression.wasp (opens new window with default values)

Title produced by software: Multiple Regression

Date of computation: Fri, 24 Dec 2010 13:28:49 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/24/t1293197225mwanlz3njiqst8m.htm/, Retrieved Fri, 24 Dec 2010 14:27:08 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/24/t1293197225mwanlz3njiqst8m.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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98.1 102.8 104.7 95.9 94.6 113.9 98.1 102.8 104.7 95.9 80.9 113.9 98.1 102.8 104.7 95.7 80.9 113.9 98.1 102.8 113.2 95.7 80.9 113.9 98.1 105.9 113.2 95.7 80.9 113.9 108.8 105.9 113.2 95.7 80.9 102.3 108.8 105.9 113.2 95.7 99 102.3 108.8 105.9 113.2 100.7 99 102.3 108.8 105.9 115.5 100.7 99 102.3 108.8 100.7 115.5 100.7 99 102.3 109.9 100.7 115.5 100.7 99 114.6 109.9 100.7 115.5 100.7 85.4 114.6 109.9 100.7 115.5 100.5 85.4 114.6 109.9 100.7 114.8 100.5 85.4 114.6 109.9 116.5 114.8 100.5 85.4 114.6 112.9 116.5 114.8 100.5 85.4 102 112.9 116.5 114.8 100.5 106 102 112.9 116.5 114.8 105.3 106 102 112.9 116.5 118.8 105.3 106 102 112.9 106.1 118.8 105.3 106 102 109.3 106.1 118.8 105.3 106 117.2 109.3 106.1 118.8 105.3 92.5 117.2 109.3 106.1 118.8 104.2 92.5 117.2 109.3 106.1 112.5 104.2 92.5 117.2 109.3 122.4 112.5 104.2 92.5 117.2 113.3 122.4 112.5 104.2 92.5 100 113.3 122.4 112.5 104.2 110.7 100 113.3 122.4 112.5 112.8 110.7 100 113.3 122.4 109.8 112.8 110.7 100 113.3 117.3 109. etc...

Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits! Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 5 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Multiple Linear Regression - Estimated Regression Equation y[t] = + 60.5979205836162 + 0.27766008955589y1[t] -0.0968386935292209y2[t] + 0.223192273494244y3[t] + 0.00965031680418547y4[t] + e[t] Multiple Linear Regression - Ordinary Least Squares Variable Parameter S.D. T-STAT H0: parameter = 0 2-tail p-value 1-tail p-value (Intercept) 60.5979205836162 20.885604 2.9014 0.005214 0.002607 y1 0.27766008955589 0.130195 2.1326 0.037125 0.018563 y2 -0.0968386935292209 0.136263 -0.7107 0.480087 0.240043 y3 0.223192273494244 0.138148 1.6156 0.111515 0.055758 y4 0.00965031680418547 0.134956 0.0715 0.943236 0.471618 Multiple Linear Regression - Regression Statistics Multiple R 0.340153663156316 R-squared 0.115704514558661 Adjusted R-squared 0.0557522782575528 F-TEST (value) 1.92994493112049 F-TEST (DF numerator) 4 F-TEST (DF denominator) 59 p-value 0.117323585280604 Multiple Linear Regression - Residual Statistics Residual Standard Deviation 9.8710825815571 Sum Squared Residuals 5748.85800858327 Multiple Linear Regression - Actuals, Interpolation, and Residuals Time or Index Actuals Interpolation Forecast Residuals Prediction Error 1 98.1 101.319425575226 -3.21942557522621 2 113.9 102.175054090614 11.7249459093861 3 80.9 106.678082833422 -25.778082833422 4 95.7 94.917909232965 0.78209076703493 5 113.2 105.704036877086 7.49596312291408 6 105.9 101.917005760278 3.9829942397224 7 108.8 101.180195162935 7.61980483706507 8 102.3 106.741021360262 -4.44102136026155 9 99 103.194975514479 -4.19497551447878 10 100.7 103.484959007347 -2.78495900734703 11 115.5 102.853784989258 12.646215010742 12 100.7 105.999266973927 -5.29926697392731 13 109.9 100.804265803754 9.09573419624593 14 114.6 108.111602478183 6.48839752181733 15 85.4 105.365267959614 -19.9652679596136 16 100.5 98.7129957124394 1.78700428756058 17 114.8 106.871139515808 7.92886048419194 18 116.5 102.907556627114 13.5924433728862 19 112.9 105.083199540972 7.81680045902818 20 102 107.256366734282 -5.25636673428184 21 106 105.095917450068 0.904082549932102 22 105.3 106.475012921748 -1.17501292174781 23 118.8 103.425759163359 15.3742408366405 24 106.1 108.029538098646 -1.9295380986458 25 109.3 103.078299274412 6.22170072558772 26 117.2 108.203003439222 8.9969965607784 27 92.5 107.382371730899 -14.8823717308992 28 104.2 100.350798091756 3.84920190824368 29 112.5 107.78543684411 4.71456315589008 30 122.4 103.520391220577 18.8796087794229 31 113.3 107.838451725707 5.46154827429279 32 100 106.318446421421 -6.31844642142051 33 110.7 105.796500478511 4.90349952148915 34 112.8 108.119906508261 4.68009349173868 35 109.8 104.610543555174 5.18945644482551 36 117.3 105.834010142988 11.4659898570118 37 109.1 108.778939059388 0.321060940612258 38 115.9 105.126524968366 10.7734750316337 39 96 109.45368196508 -13.4536819650803 40 99.8 101.511943800298 -1.71194380029795 41 116.8 105.932717003808 10.8672829961916 42 115.7 105.90904740258 9.79095259741955 43 99.4 104.613452848947 -5.21345284894706 44 94.3 104.025055805326 -9.72505580532626 45 91 104.106003937945 -13.106003937945 46 93.2 100.034953572969 -6.8349535729688 47 103.1 99.6697926999093 3.43020730009068 48 94.1 101.419831342516 -7.319831342516 49 91.8 98.4213644268072 -6.62136442680722 50 102.7 100.885128667154 1.81487133284612 51 82.6 102.221160313344 -19.6211603133435 52 89.1 94.9844556735272 -5.88445567352721 53 104.5 101.146304048015 3.35369595198453 54 105.1 100.411841675168 4.68815832483245 55 95.1 100.3439002585 -5.24390025849954 56 88.7 101.009084217862 -12.3090842178617 57 86.3 100.482976822877 -14.1829768228772 58 91.8 98.2102277016701 -6.41022770167014 59 111.5 98.4448373402927 13.0551626597074 60 99.7 102.7847048062 -3.08470480619999 61 97.5 98.8049902308031 -1.30499023080314 62 111.7 103.786799147685 7.91320085231538 63 86.2 105.499059958953 -19.2990599589529 64 95.4 96.438721487186 -1.03872148718605 Goldfeld-Quandt test for Heteroskedasticity p-values Alternative Hypothesis breakpoint index greater 2-sided less 8 0.82991480519594 0.34017038960812 0.17008519480406 9 0.798040442983934 0.403919114032131 0.201959557016066 10 0.686996723193065 0.626006553613869 0.313003276806935 11 0.757800565083879 0.484398869832242 0.242199434916121 12 0.661294332590711 0.677411334818578 0.338705667409289 13 0.654017250509373 0.691965498981253 0.345982749490627 14 0.663309500435914 0.673380999128172 0.336690499564086 15 0.705127069948046 0.589745860103908 0.294872930051954 16 0.628053123846523 0.743893752306954 0.371946876153477 17 0.575231269855698 0.849537460288605 0.424768730144302 18 0.696538705207561 0.606922589584878 0.303461294792439 19 0.683485245246839 0.633029509506323 0.316514754753162 20 0.618117550839415 0.76376489832117 0.381882449160585 21 0.579353473945914 0.841293052108173 0.420646526054086 22 0.502439888524176 0.995120222951647 0.497560111475824 23 0.627007383767645 0.74598523246471 0.372992616232355 24 0.550170468170604 0.899659063658793 0.449829531829396 25 0.515911293503391 0.968177412993219 0.484088706496609 26 0.522364513199622 0.955270973600755 0.477635486800378 27 0.573312674948786 0.853374650102428 0.426687325051214 28 0.51019538366659 0.97960923266682 0.48980461633341 29 0.446712730612908 0.893425461225815 0.553287269387092 30 0.645412424408368 0.709175151183263 0.354587575591632 31 0.603070058499436 0.793859883001128 0.396929941500564 32 0.539523504511814 0.920952990976373 0.460476495488186 33 0.497506506919947 0.995013013839895 0.502493493080053 34 0.448662031742891 0.897324063485781 0.55133796825711 35 0.404831524236407 0.809663048472814 0.595168475763593 36 0.463240869927506 0.926481739855012 0.536759130072494 37 0.396317119224367 0.792634238448734 0.603682880775633 38 0.517324454596569 0.965351090806861 0.482675545403431 39 0.508010768607009 0.983978462785983 0.491989231392991 40 0.469196984544606 0.938393969089213 0.530803015455394 41 0.570977416373508 0.858045167252983 0.429022583626492 42 0.813316820488018 0.373366359023964 0.186683179511982 43 0.808981517504465 0.38203696499107 0.191018482495535 44 0.783360295935548 0.433279408128904 0.216639704064452 45 0.771071096988574 0.457857806022851 0.228928903011426 46 0.747540591491066 0.504918817017867 0.252459408508934 47 0.69900746352573 0.60198507294854 0.30099253647427 48 0.657065960055783 0.685868079888434 0.342934039944217 49 0.599767457016662 0.800465085966677 0.400232542983338 50 0.504407932055155 0.99118413588969 0.495592067944845 51 0.634666307338715 0.73066738532257 0.365333692661285 52 0.58168282439732 0.83663435120536 0.41831717560268 53 0.465330490546769 0.930660981093538 0.534669509453231 54 0.427123544514592 0.854247089029185 0.572876455485408 55 0.338076957562247 0.676153915124493 0.661923042437753 56 0.469255693420774 0.938511386841548 0.530744306579226 Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity Description # significant tests % significant tests OK/NOK 1% type I error level 0 0 OK 5% type I error level 0 0 OK 10% type I error level 0 0 OK

Charts produced by software:

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Parameters (Session):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

Parameters (R input):

par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;

R code (references can be found in the software module):

library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }

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